Upp í vindinn - 01.05.1999, Blaðsíða 30

... UPP I VINDINN
had travelled all the way to Iceland from England without being
altered or disintegrated underway. The total precipitation in a
duration of time between 30 and 120 minutes is almost a linear
extrapolation, of the 20 minute rain. The normal behaviour is
that the total precipitation in a duration of time varies approxi-
mately with the square root of the duration. Had the variation in
table 1 been like that, the 120 minute rain would have been 14
mm instead of 28. Therefore the highest points in the 120 and
60 minute duration’s are outliers while the 30 minute value is
not exceptional, it should have been 7 instead of 9.
Table 1. Largest recorded rainshower in Reykjavík August 16 1991.
10 min. 3.4 mm
20 min. 5.7 mm
30 min. 9.2 mm
60 min. 17.3 mm
120 min. 28.4 mm
As the outlier points are only two, it does not change anything
if they are included or not, so in the following analysis they are
not discarded. By accepting that all the data in fig. 2 follows
Gumbel’s distribution it is shown that (8), which is originally
derived from 24h data only, is indeed valid for all durations. In
table 2 we see that the value is 0.217 on the average. This will
be discussed later in more detail. When (8) is inserted into ( 1)
it is possible to calculate intensity values for all return periods
when the 5 year value is known.
4 Intensity - duration -relationship g
The actual intensity values for different durations in the
records are listed in table 2. We use the five year values to build
a functional relationship between intensity and duration.
Table 2. Calculated M5 total precipitation for different duration's (IMB)
Duration Max. [mm] Mean [mm] St.dev [mm] M5 [mm] G
10 min. 4.60 2.30 0.80 3.0 0.215
20 min. 6.00 3.50 1.13 4.5 0.203
30 min. 9.20 4.46 1.52 5.7 0.213
60 min. 17.30 6.69 2.30 8.6 0.215
120 min. 28.40 9.77 3.76 12.9 0.235
0.217
Fig 3 shows two series of points. First there are the measured
values in table 2. Then there are points from the empirical for-
mula.
r=VrX
("lR--'nR>) +c3
(9)
To calculate the points the value 0.001 was used for C3. The
only thing C3 does is to control how smoothly the line in fig. 3
changes slope.
The Ra and Rb are the functions:
Ra = 0,7642*tr0,5908 duration in minutes
Rb = 6,4722*tr0-25232 (10)
Ra and Rb are total rain values, to obtain the intensity one has
to divide with the duration tr
Fig. 3 shows that the relation (10) approximates the observa-
tions very closely. It is therefore used to calculate the function
g(tf) as follows.
g= 0,02474
VrTr^
t.
+ 0,001
(11)
When (8) and (11) are inserted in (1), rain for any return peri-
od and duration may be calculated. Fig. 4 shows the result for
M5 = 100 mm/24h
Fig 4 Rain intensity for various duration and return period,
M5 = 100 mm/24h
The rain intensity values calculated above compare favourably
to the observations in the research area of the Reykjavik’s City
Engineer in Breidholt Reykjavik 0onas Eliasson 1996). These
results have been compiled by the Vatnaskil Consulting
Engineers in Reykjavik. Fig. 5 compares the two results. Note
that the result is no longer in mm but liter/second/hectare (1
hectare = 10000 m2).
The two relationships are alrnost the same although they are
Fig. 3 Total rain as function of duration
30
Fig. 5 Rainfall intensity - duration relationships, VVHI and
Vatnaskil.